EP0153614B1 - Process and device for determining the positive and negative phase sequence components of current in an unbalanced 3-phase system - Google Patents

Description

The present invention relates to a method and an arrangement for determining the co-component and counter-component current in an asymmetrically loaded network according to the preamble of claims 1 and 5.

The current that a generator supplies to the grid is generally the same in all phases. The phase shift between the currents is also usually the same and is 120 degrees in three-phase systems. If the load on the network is unbalanced, if a phase is interrupted or if the operating conditions are abnormal, such as single or two-phase short circuits, the currents become unbalanced. It is known that three-phase machines of various types are very sensitive to unbalanced loads and can be destroyed by large unbalanced loads.

The so-called counter-component current is a measure of the degree of unbalanced load. This is an imaginary symmetrical three-phase current system with reverse phase sequence. By adding this counter-clockwise current system with a second symmetrical three-phase current system with a normal phase sequence, the so-called co-component current (clockwise or co-rotating system), the currents of which have the same or a different amplitude than that of the counter-clockwise system, you get the real, the skewed load representing asymmetrical system. In other words: the asymmetrical three-phase current system can be broken down into a clockwise and a left-handed symmetrical current system with different, i.e. left-handed or right-handed phase sequence. Accordingly, the opposing current system generates an opposing magnetic rotating field (stator MMK), the speed of which in relation to the stator is the same as that of the normal rotating field, but which rotates in the opposite direction. This so-called inverse rotating field therefore induces voltages of twice the mains frequency in the rotor. These voltages drive in the metal parts of the rotor, such as. B. the damper winding, relatively large currents of twice the mains frequency. The heat generated by this causes the rotor to be damaged if the counter-component current is large enough and is effective long enough.

In order to protect a machine against damage due to unbalanced load, there is a so-called counter-component current protection, which is based on the measurement of the counter-component current. To determine the counter-component current, the known counter-component current protection devices contain a measuring arrangement in the form of a filter, which is constructed from resistors and inductors or capacitors.

The procedure for splitting an unbalanced three-phase current into the symmetrical counter-component current system and co-component current system differs depending on whether the network is grounded or not. If the network is not grounded, the unbalanced current system (unbalanced load system) - as explained above - breaks down into a counter-rotating system and a co-rotating system. FIG. 1 shows the vector diagram of the currents for an asymmetrical load, while FIG. 2 shows the corresponding positive and negative system with the specified phase sequence for a non-earthed network.

In the case of an unbalanced load, a zero component current still occurs in the case of an earthed network, which means that when the unbalanced load currents are broken down, there is also a zero system that consists of three single-phase currents that are identical in size and phase. FIG. 3 shows in the right part the three current systems into which an asymmetrical current system (on the left in FIG. 3) can be broken down when the network is grounded.

Since the phase currents of the opposite system are equally large, it is sufficient to determine one of them. In a non-earthed network, as will be described, the counter component current or a variable proportional to this current can be measured using two phase currents of the network. In a grounded network - as can be seen from the following (see Figure 8) - all phase currents must be measured in a special circuit to determine the counter component current.

The phase currents are broken down to obtain a measure of the counter-component current in accordance with known technology by means of so-called counter-component current filters. Such a filter is described in SE-A-3 69 232 (US-A-3 699 441). A variant of this filter will be described in more detail. The circuit of the filter is shown in Figure 4. It includes an active resistance Ri, which is parallel to an inductance L _i . A current corresponding to the phase current Ir flows through this parallel connection, as a result of which a voltage U ₁ occurs at the parallel connection. The filter also includes a series connection of an inductor L ₂ and an active resistor R ₂ , through which a current corresponding to the phase current I _R flows. The voltage occurring at the series connection is designated U ₂ . By suitable dimensioning of the circuit elements of the filter it can be achieved that the output signal U of the filter is zero when the network is loaded symmetrically, that is to say there is no counter component current. If, on the other hand, a counter component current is present, then the output signal U takes on a value which is proportional to the counter component current.

In the case of a symmetrically loaded network, all phase currents I _R , I _S , I _{T have the} same size and are 120 degrees out of phase with one another (see FIG. 5). If one makes the phase current I _R the reference phase, the real part I _R R _{2 of} the voltage U _{2 is} in phase with the current I _R and the imaginary part I _R X _L2 is 90 degrees out of phase with I _R. Since the reactance X _{L2 is} frequency dependent, the locus for I _R X _{I-2 is} a straight line on which the value for I _R X _L2 for the nominal frequency f _n , 0.8 - f _n and 1.2 f _{n is} entered .

In the current directions shown in FIG. 4, the phase current -Ir, ie - I _{R <} 120 degrees, must be used to determine U ₁ . The locus for U ₁ is then a semicircle, on the circumference of which the end point of the vector U ₁ for the nominal frequency f _n , 0.8 - f _n and_1.2 · f _{n is} entered.

With suitable dimensioning and trimming, U ₁ = U ₂ , and since U is the voltage between the end points of the vectors U ₁ and U ₂ , U = zero.

When examining the conditions in the case of asymmetrical loading, the counter-component current diagram according to FIG. 2 can be used. If, as in Figure 6, I _R. to the reference phase, the voltage U _{2 is formed} in the same way as in the symmetrical case described above. Because of the reverse phase sequence of the counter-component current and the current direction for I _{T shown} in FIG. 4, here too -I _T -, ie -I _R <240 degrees, must be assumed. The locus for U ₁ is the semicircle shown in Figure 6. The output signal U of the filter is shown in the figure, and the magnitude of the vector (absolute value) is proportional to the counter component current and thus a measure of this current.

FIG. 7 shows the supply of the counter-component current filter of the type described for an ungrounded network. In addition to the current transformers S _R and S _T , intermediate transformers M _R and Ms are present.

In a grounded system have a possibly all phase currents are measured on passing zero sequence current, which is done by the current transformers S _R, Ss and S _T (see Figure 8) for the elimination. There are also intermediate transformers M ₁ and M ₂ .

Counter-component current filters, such as the one described above and those described in SE-A-369 232, have certain disadvantages. As can be seen from FIG. 5, the filter delivers an output signal even when the network is loaded symmetrically when the frequency changes, since then U ₁ and U _{2 are} no longer the same size. Even in the case of transient processes in the network, the filter can deliver an output signal without a counter component current being present in the network. Furthermore, harmonics present in the network can result in the filter supplying an output signal due to different frequency responses in the three phases. Such false indications can cause a false alarm, a blockage or a trigger.

From the publication "Messtechnik", Bond 77, No. 59, July / August, 1969 pages 192 to 195, a method for determining the symmetrical current components in earthed and ungrounded networks is known, according to which the co-component current and the counter-component current from measured active power and reactive power values are calculated. The implementation of this method requires relatively complex active and reactive power meters, and the accuracy of the method depends on the voltage symmetry of the three-phase network.

The invention has for its object to develop a method of the type mentioned, in which the determination of the counter-component current required for counter-component current protection can be carried out without inductors or capacitors and without active and reactive power measuring devices.

To achieve this object, a method is proposed according to the preamble of claim 1, which according to the invention has the features mentioned in the characterizing part of claim 1.

Advantageous embodiments of the method are mentioned in the further claims 2 to 4.

The invention is also based on the object of developing an arrangement for carrying out a method of the type mentioned at the beginning, in which the determination of the counter-component current required for counter-component current protection is carried out without inductors or capacitors and without active and reactive power measuring devices.

To solve this problem, an arrangement according to the preamble of claim 5 is proposed, which according to the invention has the features mentioned in the characterizing part of claim 5.

Advantageous embodiments of the arrangement are mentioned in claims 6 to 7.

As can be seen from the above explanations, the current of each phase can be broken down into a counter-component current and a co-component current and - with an earthed network - additionally into a zero-component current in the case of an asymmetrically loaded network. In a system according to FIGS. 1 and 2, I _{R1 is} in the components i _{R +} and I _R. disassembled, which form an angle e between them (see Figure 9). The relationship between I _R1 , I _{R +} and I _R. can be described using the cosine theorem. A corresponding breakdown can be carried out for phases S and T. For the current components obtained in this way, | I _{R +} | applies = | I _{S +} | = | I _{T +} | = 11 ₁₁ and | I _R- | = | I _S- | = | I _T- | = | I ₂ |, the phase shift between the co-component and counter-component currents being 120 degrees. 1 _{1 is} the amount of the co-component and 1 _{2 is} the amount of the counter component.

For the phase R ailt;

Entsprechende Gleichungen lassen sich für die Phasen S und T aufstellen, so daß man ein Gleichungssystem aus drei Gleichungen mit drei Unbekannten bekommt. Man kann daher durch Messung aller Phasenströme eine Anordnung schaffen, durch welche sowohl der Mit- wie Gegenkomponentenstrom sowie der Winkel berechnet werden können.

Corresponding equations can be set up for phases S and T, so that an equation system consisting of three equations with three unknowns is obtained. One can therefore create an arrangement by measuring all phase currents, by means of which both the co-component and counter-component current and the angle can be calculated.

• Figur 1 ein Beispiel für die in einem unsymmetrisch belasteten Netz auftretenden Ströme,
• Figur 2 die Zerlegung der Phasenströme gemäß Figur 1 in Gegenkomponentenströme und Mitkomponentenströme bei einem nicht geerdetem Netz,
• Figur 3 eine entsprechende Darstellung wie in den Figuren 1 und 2 für ein geerdetes Netz, wobei zusätzlich Nullkomponentenströme auftreten,
• Figur 4 eine Ausführungsform eines Gegenkomponentenstromfilters,
• Figur 5 die Zusammensetzung des Ausgangssignals des Filters bei einem symmetrisch belasteten Netz,
• Figur 6 die Zusammensetzung des Ausgangssignals des Filters, welches ein Maß für den Gegenkomponentenstrom im Netz ist, für ein nicht geerdnetes unsymmetrisch belastets Netz,
• Figur 7 die Stromspeisung des Filters zur Gegenkomponentenstrommessung in einem nicht geerdeten Netz,
• Figur 8 Stromspeisung des Filters zur Gegenkomponentenstrommessung in einem geerdeten Netz,
• Figur 9 die Zerlegung eines Phasenstromes I_R1 in den Gegenkomponentenstrom I_R. und den Mitkomponentenstrom I_R+_'
• Figur 10 ein Blockschaltbild zur Berechnung des Mit- und Gegenkomponentenstroms,
• Figur 11 ein Blockschaltbild zur digitalen Berechnung des Mit- und des Gegenkomponentenstroms,
• Figur 12 die Schaltung der Zwischentransformatoren, durch welche die Meßanordnung unabhängig davon gemacht wird, ob das Netz geerdet ist oder nicht.

The invention will be described in more detail with reference to the other figures. The figures show

• FIG. 1 shows an example of the currents occurring in an asymmetrically loaded network,
• 2 shows the decomposition of the phase currents according to FIG. 1 into counter-component currents and co-component currents in the case of a non-earthed network,
• 3 shows a representation corresponding to that in FIGS. 1 and 2 for a grounded network, zero component currents additionally occurring,
• FIG. 4 shows an embodiment of a counter component current filter,
• FIG. 5 shows the composition of the output signal of the filter in a symmetrically loaded network,
• FIG. 6 shows the composition of the output signal of the filter, which is a measure of the counter-component current in the network, for a non-grounded unbalanced network,
• FIG. 7 shows the current supply of the filter for counter-component current measurement in an ungrounded network,
• FIG. 8 current supply of the filter for counter-component current measurement in an earthed network,
• FIG. 9 shows the decomposition of a phase current I _R1 into the counter component current I _R. and the co-component current I _R + _'
• FIG. 10 shows a block diagram for calculating the co-component and counter-component current,
• FIG. 11 shows a block diagram for the digital calculation of the co-current and the counter-component current,
• FIG. 12 shows the circuit of the intermediate transformers, by means of which the measuring arrangement is made regardless of whether the network is grounded or not.

• I_S ² - IR = 2 I₁·I₂ cos e - 2 I₁·I₂ cos (θ -120°) (4)

The system of equations for all phase currents is:

• I _S ² - IR = 2 · I ₁ I ₂ cos e - 2 I ₁ I ₂ · cos (θ -120 °) (4)

Mit Hilfe trigonometrischer Umwandlungsformeln und Einsetzen der Werte für sin 120° und cos 120° können die Gleichungen (4) und (5) wie folgt geschrieben werden:

Equation (3) - (1) gives:

Using trigonometric conversion formulas and inserting the values for sin 120 ° and cos 120 °, equations (4) and (5) can be written as follows:

By adding equation (6) and equation (7) one obtains:

By introducing equation (8b) and equation (1) we get:

By forming the difference from equations (6) one obtains:

The quotient from equations (10) and (8a) results after certain conversions:

By solving equation (10) according to 1 ₁ and inserting it into equation (1), one obtains after appropriate transformation:

By inserting tan e according to equation (11) one obtains:

Equation (13) is solved according to sin ² e with the help of equation (11) and, after inserting it into the trigonometric relationship:

Inserting this value in equation (13) after transformation results in:

setzt, geht Gleichung (15) über in

By:

equation (15) passes into

The resolution after 1 ₂ results in:

The sign to be used under the root sign in equation (20) is determined by the phase sequence of the network. It can be shown that equation (20) can also be used to calculate the co-component current h. The relationships between the type of sign under the root, the phase sequence, the co-component current and the counter-component current are shown in the following table:

The arithmetic operations required to calculate 1 ₁ and / or 1 ₂ when the phase sequence of the network is known are relatively simple and can be carried out in many different ways. A calculation flow diagram for such a calculation circuit is shown in FIG. 10. The circuit contains squares 1R, 1S, 1T, 2R, 2S, 2T and 3, multiplication elements 4, 5 and 6, summation elements 7, 8, 9 and 10, elements 11 and 12 for summation and absolute value formation as well as elements 13 and 14 for square rooting of input signals. The phase sequence is determined by the link 15. The arithmetic operations mentioned can be carried out in analog, digital or mixed analog-digital form. The calculation flow diagram according to FIG. 10 can also be understood as a block diagram of an analog circuit arrangement. Completion can be done by analog RMS formation of the input signals (RMS means "root mean square" value = root mean square, ie effective value).

Figure 11 shows an embodiment in purely digital technology. The analog input signals of the phase currents I _R , 1 ₅ , I _T are converted into digital values in analog-digital converters 16R, 16S and 16T. The phase currents converted into digital values are RMS treated in the RMS elements 17R, 17S and 17T and passed on to a suitably designed processor 18 for the calculation of equation (20), to which information about the phase sequence present is also supplied via the element 15.

The invention comprises various embodiments with a smaller or greater degree of integration of the links 15 to 18 according to FIG. 11.

The same applies to hybrid solutions from a mixture of analog and digital technology for the various links and functions.

If a determined co-component or counter component current exceeds a preset value, a trigger signal can be obtained. Triggering can also simply take place according to different invert time curves.

As can be seen from the above description, all phase currents must always be supplied to the measuring arrangement according to the invention. In order not to have to work with different input circuits, depending on whether the network is grounded or not, a circuit is used in accordance with the prior art, which is constructed in principle like that shown in Figure 8, but in which the primary and the secondary side are interchanged. This circuit is shown in FIG. 12, in which the three phase currents are converted into an equivalent three-phase system without a zero component.

Claims (7)

1. Method for determining the positive phase sequence current components 1₁ and/or the negative phase sequence current components 1₂ in an unbalanced three-phase grounded or non-grounded network with measuring the phase currents I_R, Is, IT and the phase sequence (RST, RTS), characterized in that the positive phase sequence current component 1₁ and/or the negative phase sequence current component 1₂ are calculated from the phase current measuring values, which in the case of a grounded network are first separated from a portion originating from a possible zero sequence current component, and the measuring value of the phase sequence according to the formula

with

and

and I_R, Is, IT being the measured phase currents after separation of any possible zero phase sequence current.

2. Method according to claim 1, characterized in that in the case of the phase sequence RST the plus sign in said square root expression is used to determine the positive phase sequence current and the minus sign is used to determine the negative phase sequence current.

3. Method according to claim 1, characterized in that in the case of the phase sequence RTS the plus sign in said square root expression is used to determine the negative phase sequence current and the minus sign is used to determine the positive phase sequence current.

4. Method according to any of the preceding claims, characterized in that the positive phase sequence current and/or the negative phase sequence current are/is obtained with the help of a direct non-iterative method.

5. Device for determining the positive phase sequence current components I₁ and/or the negative phase sequence current components 1₂ in an unbalanced three-phase grounded or non-grounded network with members for measuring the phase currents I_R, Is, IT and the phase sequence (RST, RTS), characterized in that at least in the case of a grounded network means are provided for separating the phase current measuring values from those portions which originate from a possible zero sequence current component, and that calculating members are provided in which the positive phase sequence current component t, and/or the negative phase sequence current component 1₂ are calculated from the phase current measuring values, after their separation from a possible zero sequence current component, and the measuring value of the phase sequence according to the formula

with

and

and I_R, Is, IT being the measured phase currents after separation of any possible zero phase sequence current.

6. Device according to claim 5, characterized in that the calculating members comprise squaring members (1R, 1S, 1T, 2R, 2S, 2T, 3), multiplying members (4, 5, 6), summation members (7, 8, 9, 10), members (11, 12) for adding and forming of the absolute value, and members (13, 14) for forming the square root.

7. Device according to any of claims 5 or 6, characterized in that the circuit comprises analog-digital converters (16R, 16S, 16T), members (17R, 175, 17T) for forming the RMS-value and members (18) for the numerical calculation of an algebraic expression.

Images